Generally speaking, alpha refers to internal playtesting, beta is external or public playtesting.

A map is in alpha if it is only being tested by the mapper(s) or their friends. Personally I would guess that tests on tf2maps servers would also be withing the range of alpha. At this stage a map would be expected to be at a certain level of incompleteness and subject to major changes. Alpha is the first stage of building, there is no pre-alpha except drawings. A map can go through as many iterations of alpha as it needs to become....

Beta. A map in beta version means that it is ready to be released to public servers. There are several community servers that will accept custom maps in beta. A beta map should already be looking polished and playable. Issues such as balance and exploits could be looked at here. Beta should continue until there are no further playing issues to be corrected.

RC1 is saying 'this map is ready to be released, but I am not calling to final for a few weeks in case any problems arise that have gone unnoticed.' RC stands for Release Candidate btw.

If anything comes up and needs to be changed, go to RC2 and so on.

If the RC is good to go, it becomes the release map. Release it by it's full name. Don't add 'final' to the end, just the name of the map.

Alpha testing will be layout testing. Making sure choke points arn't too OP, correcting scale and scenario features effect on gameplay etc. Generally there will be little to no detail unless it is focal to the objective(s). Refining objective timers and victory conditions.

Beta testing is generally the detail pass. Creating a theme, making sure the details work, are immersive, and are player clipped properly.